A technique of representation of a 3-D object using a Mesh Model is already disclosed by H. DELINGETTE in the publication entitled “Simplex Meshes: a General Representation for 3-D shape Reconstruction” in “Processing of the International Conference on Computer Vision and Pattern Recognition (CVPR'94), 20-24 Jun. 1994, Seattle, USA”.
In this paper, a physically based approach for recovering three-dimensional objects is presented. This approach is based on the geometry of “Simplex Meshes”. Elastic behavior of the meshes is modeled by local stabilizing functions controlling the mean curvature through the simplex angle extracted at each vertex (node of the mesh). Those functions are viewpoint-invariant, intrinsic and scale-sensitive. Unlike deformable surfaces defined on regular grids, Simplex Meshes are very adaptive structures. A refinement process for increasing the mesh resolution at highly curved or inaccurate parts is also disclosed. Operations for connecting Simplex Meshes in order to recover complex models may be performed using parts having simpler shapes.
A Simplex Mesh has constant vertex connectivity. For representing 3-D surfaces, Simplex Meshes, which are called 2-Simplex Meshes, where each vertex is connected to three neighboring vertices, are used. The structure of a Simplex Mesh is dual to the structure of a triangulation as illustrated by the FIG. 1 of the cited publication. It can represent all types of orientable surface. The contour on a Simplex Mesh is defined as a closed polygonal chain consisting of neighboring vertices on the Simplex Mesh. The contour is restricted to not intersect itself, as far as possible. Contours are deformable models and are handled independently of the Simplex Mesh where they are embedded.
Four independent transformations are defined for achieving the whole range of possible mesh transformations. They consist in inserting or deleting edges in a face of the Mesh. The description of the Simplex Mesh also comprises the definition of a Simplex Angle that generalized the angle used in planar geometry; and the definition of metric parameters, which describe how the vertex is located with respect to its three neighbors.
The dynamic of each vertex is given by a Newtonian law of motion. The deformation implies a force that constrains the shape to be smooth and a force that constrains the mesh to be close to the 3-D object. Internal forces determine the response of a physically based model to external constraints. The internal forces are expressed so that they are intrinsic viewpoint invariant and scale dependant. Similar types of constraints hold for contours.
Hence, the cited publication provides a simple model for representing a given 3-D object. It defines the forces to be applied in order to reshape and adjust the model onto the 3-D object of interest. The “Simplex Mesh technique” is a robust segmentation method.